Abstract The paper introduces a novel framework for small area estimation based on spatio-temporal M-quantile regression. The proposed approach extends the Geographically Weighted Regression by incorporating both spatial and temporal weighting schemes, and integrates them with the M-quantile modelling to effectively capture local distributional features across space and time. The resulting predictors are specifically designed for out-of-sample prediction in small domains and are accompanied by analytical estimators of their mean squared error. The methodology is evaluated through extensive simulation studies, demonstrating strong robustness to spatio-temporal dependence and the presence of outliers at both unit and area levels. An application to county-level air quality data in the United States (2016–2023) highlights the predictive performance and practical relevance of the proposed methods.
Bugallo et al. (Wed,) studied this question.